Nonlinear Dynamics, Bifurcation, Basin Analysis, and Chaos Control in an Asymmetric-Cost Bertrand Duopoly Model

This paper investigates a dynamic Bertrand duopoly model with boundedly rational firms under asymmetric cost structures. Unlike classical formulations based on symmetric costs, we consider a heterogeneous market where one firm faces a quadratic cost function and the other a linear cost structure. We analyze the existence and local stability of the Bertrand–Nash equilibrium, revealing how adjustment speeds and cost asymmetry influence market stability. The results show that excessive price adjustments and increasing cost differences can destabilize the equilibrium through a period-doubling route to chaos, generating unpredictable price dynamics. The chaotic behavior is characterized using bifurcation analysis, Lyapunov exponents, basin of attraction analysis, and the 0–1 chaos test. Furthermore, a feedback control strategy is developed to suppress chaotic fluctuations and restore the Nash equilibrium. By integrating asymmetric cost structures, global stability analysis, chaos detection, and control mechanisms within a Bertrand framework, this study extends existing symmetric-cost models and provides new insights into stabilizing competitive markets. Numerical simulations confirm the theoretical findings and highlight the role of cost heterogeneity and adjustment mechanisms in shaping the stability and predictability of price competition.